First Week Final Test

0

0

Correct

Right!

$\forall C \; \forall n \in \mathbb{N}\, \exists \varepsilon>0 \Rightarrow |a_n-C|>\varepsilon$

$\exists\varepsilon >0 \; \forall N \in \mathbb{N}\; \exists n>N \Rightarrow |a_n-C|>\varepsilon$

$\exists>0 \; \exists n> N \Rightarrow |a_n-C|>\varepsilon$

Nothing of the above

Correct

Correct!

Question 3

Fill in the blancs: "Let us prove that $\sqrt{2}+\sqrt{3}$ is not *****. Assume the opposite: $\sqrt{2}+\sqrt{3}=\frac{m}{n}$ , where $m$ is ***** and $n$ is *****. Squaring both sides, we get $5+2\sqrt{6}=\frac{m^2}{n^2}$ , or $\sqrt{6}=\frac{1}{2}\left(\frac{m^2}{n^2}-5\right)$ . Since $\frac{1}{2}\left(\frac{m^2}{n^2}-5\right)$ is ***** we get equivalent to the $\sqrt{2}$ case..."

Write missing words in the order of blancs, separate with semi-colon, for each blanc there should be only one word.

1 / 1 point

rational;integer;natural;rational

Correct

shrink horizontally by $3$ ; move horizontally by $4$ ; turn the graph upside-down (multiply by $(-1)$ ); move vertically up by $2$

move horizontally by $4/3$ ; shrink horizontally by $3$ ; move vertically down by $2$ ; turn the graph upside-down (multiply by $(-1)$ )

both variants are wrong

Correct

Correct!

1999

1999

Correct

Correct!

0

0

Correct

Correct!

e^{-1}

1/E

Correct

Correct!

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